This is a fantastic question! Thanks Natja.
I hope others will help answer this one as well.
One of the tactics that helped us was to implement adult family meetings with the three of us. At the meetings, each of us felt free to discuss our needs, wants or desires and of course any family business. Some times, we would have a previously written and planned agenda, and other times, we came to the meeting without a planned agenda. I originally gleaned the idea from the Cosby Show because they held family meetings often. The meetings were definitely helpful for us.
However, together, we also planned out how we would handle our family. We discussed how the children should be handled and disciplined, financial matters, routines, chores, education, rules, employment, etc. Since we came up with plans, we had these plans as our tactics. Also, anytime something new came up, we would meet again and devise a new plan.
In said situation though, the husband should encourage each of the wives to talk to each other. If he needs to bring them together in the beginning like we did with our meetings to start the conversations between them rolling, then by all means he should. However, he needs to also slowly pull away from being the mediator by bringing the two together and saying, "SAHM wants to talk to you about providing some finances for the children. Can the two of you please discuss this and let me know what you two decided?" Then, he should leave the two alone to talk.
Just a few ideas. I hope to hear from others on this topic as well.